Occurence of fundamental mathematical constants

0, 1, phi (the Golden ratio), e, pi, delta (Feigenbaum's constant) and comparatively many other fundamental, dimensionless mathematical constants occur on the interval 0 to 5. With a potential infinity of numbers to choose from, why does such a confluence exist?

0, 1, phi (the Golden ratio), e, pi, delta (Feigenbaum's constant) and comparatively many other fundamental, dimensionless mathematical constants occur on the interval 0 to 5. With a potential infinity of numbers to choose from, why does such a confluence exist?

Maybe small ones are easy to discover. Maybe our idea of 'small' is tied to the size of these constants (no, really -- 1 is the measure by which we count, so if it were 'larger' so would be our concept of 'small').

Maybe it's just easier to find and work with small constants -- perhaps the order of the Monster group is just as fundamental, but less has been done with it since it's so large.